Multifractal analysis for studying criticality in neural dynamics
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School of Science |
Doctoral thesis (article-based)
| Defence date: 2025-05-06
Authors
Date
2025
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Degree programme
Language
en
Pages
69 + app. 85
Series
Aalto University publication series Doctoral Theses, 46/2025
Abstract
The brain criticality hypothesis suggests that the brain operates near a critical point of a phase transition between order and disorder. Scale invariance, where the properties of an object do not depend upon the scale at which it is considered, is the hallmark of critical systems and is evident in the brain both spatially and temporally, as in the case of the dynamics of observed brain oscillations. Multifractal analysis extends the characterization of scale invariance beyond the second-order properties of time series, thereby providing a measure of their temporal fluctuations in pointwise regularity. So far, multifractal analysis has received very limited attention from the neuroscientific community. This is due to its increased complexity compared to traditional approaches and the absence of a neurophysiologically grounded explanation of the results. In particular, no explicit connection has been established between the brain criticality hypothesis and multifractality in the brain. This doctoral thesis aims to bridge the gap between our understanding of brain criticality and the multifractality observed in brain dynamics. The significance of this body of work lies in its two key contributions: It is the first systematic investigation of temporal multifractality in a model for critical brain dynamics, and second, it provides the first proper characterization of multifractality in brain oscillatory dynamics at rest, using a large magnetoencephalography (MEG) dataset. The first part of this thesis introduces the fundamental constructs of brain criticality and multifractality and provides the necessary background to appreciate the significance of the three articles that make up the second section of this dissertation. The first article presents multifractality in the temporal dynamics of simulations of a model of brain criticality. The second article addresses a methodological issue in multifractal analysis by introducing an algorithm that handles outliers, which has so far been neglected when applying multifractal analysis to electrophysiological recordings of brain activity. The third article applies multifractal analysis to oscillatory brain dynamics recorded using MEG, uncovering the multifractal properties of neural oscillations for the first time. This body of work advances our understanding of how multifractality may arise within the context of critical brain dynamics, offering the possibility to both better understand the results of multifractal analysis and better characterize the scale invariance found in oscillatory dynamics.Description
Supervising professor
Palva, J. Matias, Prof., Aalto University, Department of Neuroscience and Biomedical Engineering, Finland; Ciuciu, Philippe, Research Director, Université Paris-Saclay, FranceKeywords
critical dynamics, multifractal analysis, scale invariance, complex systems, neuroimaging, neural network modeling
Other note
Parts
- [Publication 1]: Merlin Dumeur, Sheng H. Wang, J. Matias Palva, Philippe Ciuciu. Multifractality in critical neural field dynamics. Submitted to Physical Review Letters, December 2023.
- [Publication 2]: Merlin Dumeur, J. Matias Palva, Philippe Ciuciu. Outlier detection and removal in multifractal analysis of electrophysiological brain signals. Submitted to Journal of Advances in Signal Processing, December 2024.
- [Publication 3]: Merlin Dumeur, Philippe Ciuciu, Satu Palva, Wenya Liu, Maria Vesterinen, Paula Partanen, Alexandra Andersson, Samanta Knapiˇc, Satu Palva, J. Matias Palva. Characterization of multifractality in oscillatory dynamics. Submitted to Journal of Neuroscience, February 2025.